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Quantum Information Processing

New quantum codes from matrix-product codes over small fields

  • 01-08-2020
Published in:
Authors
Hao Song
Ruihu Li
Yang Liu
Guanmin Guo
Published in
Quantum Information Processing | Issue 8/2020

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Abstract

In this paper, we provide methods for constructing Hermitian dual-containing (HDC) matrix-product codes over \(\mathbb {F}_{q^2}\) from some non-singular matrices and a special sequence of HDC codes and determine parameters of obtained matrix-product codes when the input matrix and sequence of HDC codes satisfy some conditions. Then, using some nested HDC BCH codes with lengths \(n=\frac{q^4-1}{a} (a=1 ~\)or\(~ a=q\pm 1)\), we construct some HDC matrix-product codes with lengths \(N=\) 2n or 3n and derive nonbinary quantum codes with length N from these matrix-product codes via Hermitian construction. Four classes of quantum codes over \(\mathbb {F}_{q}\) (\(3\le q\le 5\)) are presented, whose parameters are better than those in the literature. Besides, some of our new quantum codes can exceed the quantum Gilbert-Varshamov (GV) bound.

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previous article Numerical detection of Gaussian entanglement and its application to the identification of bound entangled Gaussian states
next article An index theorem for split-step quantum walks
Title
New quantum codes from matrix-product codes over small fields
Authors
Hao Song
Ruihu Li
Yang Liu
Guanmin Guo
Publication date
01-08-2020
Publisher
Springer US
Published in
Quantum Information Processing / Issue 8/2020
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02722-5
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